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# If m and k are integers, is x an integer?

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Senior Manager
Joined: 20 Aug 2015
Posts: 391
Location: India
GMAT 1: 760 Q50 V44
If m and k are integers, is x an integer?  [#permalink]

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23 Feb 2016, 18:34
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85% (hard)

Question Stats:

46% (02:17) correct 54% (02:07) wrong based on 97 sessions

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If $$m$$ and $$k$$ are integers, and $$x^m = k$$, is $$x$$ an integer?

(1) $$-1 < k <2$$
(2) $$m > 0$$
Math Expert
Joined: 02 Aug 2009
Posts: 6961
If m and k are integers, is x an integer?  [#permalink]

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24 Feb 2016, 03:49
3
TeamGMATIFY wrote:
If $$m$$ and $$k$$ are integers, and $$x^m = k$$, is $$x$$ an integer?

(1) $$-1 < k <2$$
(2) $$m > 0$$

hi,

$$x^m = k$$, m and k are integers, is x an integer..

(1) $$-1 < k <2$$
since k is an integer, k=0 or 1..
so
1) x^m=0
here x will be 0 as m is an integer
or x^m=1..
here it is possible x is a fraction or non integer while m=0, and x is an integer 1, with m as any integer..
insuff

(2) $$m > 0$$
m can be any integer greater than 0, but we do not know anything about k..
m acn be 2 and x $$\sqrt{3}$$, then k will be an integer..
or m=2 and x =3 , here k will again be an integer..
so x can be a non integer or integer..
insuff.

combined..
we know m>0, so x^m=1, only when x is 1..
Suff..

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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If m and k are integers, is x an integer?  [#permalink]

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24 Feb 2016, 22:31
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If m and k are integers, and x^m=k , is x an integer?

(1) −1<k<2
(2) m>0

In the original condition, there are 3 variables(x,k,m) and 1 equation(x^m=k), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), if k is an integer not x, k=0,1, which only satisfies 1^m=1, 0^m=0. So, it is yes and sufficient.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: If m and k are integers, is x an integer?  [#permalink]

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21 Oct 2017, 13:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If m and k are integers, is x an integer? &nbs [#permalink] 21 Oct 2017, 13:45
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